Cold-press is actually brewed cold, and it takes hours to have a well-brewed batch. That is a major reason the costs are different—prep time is much longer, and there are risks associated with preparing food in advance.
Iced coffee, real iced coffee (not cold press), is crap. It's hot brewed coffee refrigerated and/or poured over ice. This messes with the composition of the liquid, and generally causes it to become bitter. (Though if it's espresso, the results are different...)
Mystery solved, perhaps?